The Work of Winkenwerder
To date, none of the evidence in favor of the topographical hypothesis completely fills these requirements. Winkenwerder (loc. cit.), in analyzing the results of telescopic counts of birds at Madison and Beloit, Wisconsin, Detroit and Ann Arbor, Michigan, and at Lake Forest, Illinois, between 1898 and 1900, plotted the number of birds seen at fifteen-minute intervals as a function of the time of the night. He believed that the high points in the resulting frequency histograms represented intervals when the field of the telescope was moving over certain topographically determined flight lanes, though he did not specify in all cases just what he assumed the critical physiographic features to be. Especially convincing to him were results obtained at Beloit, where the telescope was situated on the east bank of the Rock River, on the south side of the city. Immediately below Beloit the river turns southwestward and continues in this direction about five miles before turning again to flow in a southeastward course for approximately another five miles. In this setting, on two consecutive nights of observation in May, the number of birds observed increased tremendously in the 2 to 3 A. M. interval, when, according to Winkenwerder's interpretation of the data (he did not make the original observations at Beloit himself), the telescope was pointing directly down the course of the river. This conclusion is weakened, however, by notable inconsistencies. Since the moon rises later each evening, it could not have reached the same position over the Rock River at the same time on both May 12-13 and May 13-14, and therefore, if the peaks in the graph were really due to a greater volume of migration along the watercourse, they should not have so nearly coincided. As a matter of fact the incidence of the peak on May 12-13 should have preceded that of the peak on May 13-14; whereas his figure shows the reverse to have been true. Singularly enough, Winkenwerder recognized this difficulty in his treatment of the data from Madison, Wisconsin. Unable to correlate the peak period with the Madison terrain by the approach used for Beloit, he plotted the observations in terms of hours after moonrise instead of standard time. This procedure was entirely correct; the moon does reach approximately the same position at each hour after its rise on successive nights. The surprising thing is that Winkenwerder did not seem to realize the incompatibility of his two approaches or to realize that he was simply choosing the method to suit the desired results.
Furthermore, as shown in Part I of this paper, the number of birds seen through the telescope often has only an indirect connection with the actual number of birds passing over. My computations reveal that the highest counts of birds at Beloit on May 12-13 were recorded when the moon was at an altitude of only 8° to 15° and, that when appropriate allowance is made for the immense size of the field of observation at this time, the partially corrected flight density for the period is not materially greater than at some other intervals in the night when the telescope was not directed over the course of the Rock River. These allowances do not take the direction factor into consideration. Had the birds been flying at right angles to the short axis of an elliptical section of the cone throughout the night, the flight density in the period Winkenwerder considered the peak would have been about twice as high as in any previous interval. On the other hand, if they had been flying across the long axis at all times, the supposed peak would be decidedly inferior to the flight density at 10 to 11:00 P. M., before the cone came near the river.
Admittedly, these considerations contain a tremendous element of uncertainty. They are of value only because they expose the equal uncertainty in Winkenwerder's basic evidence. Since the coördinates of the birds' apparent pathways at Beloit were given, I at first entertained the hope of computing the flight densities rigorously, by the method herein employed. Unfortunately, Winkenwerder was apparently dealing with telescopes that gave inverted images, and he used a system for recording coördinates so ambiguously described that I am not certain I have deciphered its true meaning. When, however, his birds are plotted according to the instructions as he stated them, the prevailing direction of flight indicated by the projection formula falls close to west-northwest, not along the course of the Rock River, but at direct right angles to it.
Fig. 31. Directional components in the flight at Tampico on three nights in 1948. The lengths of the sector vectors are determined by their respective densities expressed as a percentage of the station density for that night; the vector resultants are plotted from them by standard procedure. Thus, the nightly diagrams are not on the same scale with respect to the actual number of birds involved.
Fig. 32. Hourly station density curve at Tampico, Tamaulipas, on the night of April 21-22, 1948 (CST).
Interpretation of Recent Data